Moving an iron sphere along a path with an electromagnet

So I am working on a project that requires the movement of iron nanoparticles (let's assume 25nm in diameter, and let's assume the sphere is uniform and pure iron) through a (non-magnetic) gel using an externally applied magnetic field. Let's assume the total distance I want to move the particle is 5cm. The force I need to exert on each nanoparticle individually to move them through the gel is at most 20pN. I have no physics background, but what I think I know is that to move a magnetic particle along a straight path with constant force I will need to apply a magnetic field gradient that is roughly equivalent at each point along the path. I believe this magnetic field gradient should be on the order of 50T/m.

Is it possible to achieve this using an electromagnet? Is there a name for this type of device that I can look up? How might I go about creating such a device if it is possible? I'm just looking for someone to point me in the right direction. Please assume if you post a formula that I'm a 10-year old with only a basic understanding of electromagnetism.

Staff: Mentor

50 T/m is possible, but getting this over 5 cm is not trivial. As an example, state-of-the-art LHC magnets have ~250 T/m over a few centimeters.
There are a few applications (e.g. MRI), so it might be possible to buy those magnets. Creating one yourself... I don't know. The LHC magnets are superconducting, with normal-conducting magnets it will be challenging to get high gradients and you certainly don't have the tools to make very good coils.